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 Aug 6 comment Normalization parameter, properties of Dirac delta functions @mamerel'Oye: Not quite; I've edited the post to calculate the factor. Note that you can check such things by checking dimensions. The normalization factor needs to have dimensions of reciprocal energy (for the delta) times reciprocal length (for the integral). Aug 6 revised Normalization parameter, properties of Dirac delta functions more concise form Aug 6 revised Normalization parameter, properties of Dirac delta functions calcuated full normalization factor in response to comment; deleted 241 characters in body Aug 6 comment Dealing with “at least” in Permutation @MistyD: Well, there you go. If those are the only two possibilities, all you need to do is add them up. Aug 6 comment Dealing with “at least” in Permutation @MistyD: I don't know how you got $5\cdot5$; there are only $4$ math teachers in all, so there's only one way to choose $4$ of them, not $5$ ways. On your second question: What other possibilities except for $3$ and $4$ math teachers do you see for the combination to include at least $3$ math teachers if there are $4$ math teachers in all? Aug 6 comment Proving every open set in metric space $X$ is the union of a subcollection of base You talk about a metric space in the title, but the question never mentions metric spaces and seems to be about topological spaces in general. Aug 6 revised Reference request for examples of probabilistic heuristics, help put some examples in a broader context. adapted to edit in question Aug 6 comment Reference request for examples of probabilistic heuristics, help put some examples in a broader context. @Dan: I agree. [That agreement was to a now-deleted comment about the heuristics on the twin-prime conjecture really being $0$/$1$.] In fact I've been meaning for a while now to ask a question about the distinction between these sorts of heuristics, ones that lead to finite, if often large, updates, and ones for which the heuristic probability is exactly $0$ or $1$. The Collatz conjecture is another example of the latter type. Aug 6 answered Dealing with “at least” in Permutation Aug 6 comment Reference request for examples of probabilistic heuristics, help put some examples in a broader context. @Dan: Also check out this paper linked to in the Wikipedia article, which shows that independence assumptions can be tricky. The expected number of counterexamples I cited was based on the heuristics that this paper reassesses. Aug 6 answered Reference request for examples of probabilistic heuristics, help put some examples in a broader context. Aug 6 answered Group with an automorphism of order 2 (Jacobson BA1) Aug 6 comment Can you prove why consecutive diagonal intersection points show decreasing fractions inside a rectangle? @MacGyver: How about analytic-geometry? Aug 6 comment Can you prove why consecutive diagonal intersection points show decreasing fractions inside a rectangle? @MacGyver: You're welcome. I liked the question, too :-) Aug 6 answered Can you prove why consecutive diagonal intersection points show decreasing fractions inside a rectangle? Aug 6 comment Newton's method - determine accuracy in calculation @Kristian: What threw me off was that the hint said to "restart Newton's algorithm", not to restart its analysis. If I understand correctly now, the idea is to apply Newton's algorithm in the usual way for $40$ steps and apply two different kinds of analysis to these steps. Aug 5 comment Newton's method - determine accuracy in calculation @Kristian: You're welcome. And you were right to switch the accepted answer. Aug 5 comment Newton's method - determine accuracy in calculation @Kristian: I see. By the way, you don't have to ping me under my own answer since I get notified of any comments under it anyway; but if you do want to ping someone (under a post that isn't theirs), you need to put an @ in front of the user name. Aug 5 comment Newton's method - determine accuracy in calculation @Kristian: I'm afraid I don't understand what you mean by "restarting" the algorithm. If I just apply it to $10^{10}$, I get within $10^{-8}$ of $1$ after $37$ steps. Aug 5 comment Some naive questions about embeddings Yes, everthing originates from $\mathbb N$. $\mathbb Q$ is a set of equivalence classes of pairs in $\mathbb Z$, $\mathbb R$ is a set of equivalence classes of sequences in $\mathbb Q$, and $\mathbb C$ is a set of pairs in $\mathbb R$; though all these structures can also be defined in other ways. On your second question, I guess you're right about the connotations of "embed"; but I can't off the top of my head think of a word that would have fit the concept better.